{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fa9e9f53",
   "metadata": {},
   "source": [
    "# Optimization Using Newton's Method"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14154c8a",
   "metadata": {},
   "source": [
    "In this lab you will implement Newton's method optimizing some functions in one and two variables. You will also compare it with the gradient descent, experiencing advantages and disadvantages of each of the methods."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8aff2e4d",
   "metadata": {},
   "source": [
    "# Table of Contents\n",
    "\n",
    "- [ 1 - Function in One Variable](#1)\n",
    "- [ 2 - Function in Two Variables](#2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5202ca39",
   "metadata": {},
   "source": [
    "## Packages\n",
    "\n",
    "Run the following cell to load the packages you'll need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "21767de7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.gridspec import GridSpec"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f12db316",
   "metadata": {},
   "source": [
    "<a name='1'></a>\n",
    "## 1 - Function in One Variable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d07eb61",
   "metadata": {},
   "source": [
    "You will use Newton's method to optimize a function $f\\left(x\\right)$. Aiming to find a point, where the derivative equals to zero, you need to start from some initial point $x_0$, calculate first and second derivatives ($f'(x_0)$ and $f''(x_0)$) and step to the next point using the expression:\n",
    "\n",
    "$$x_1 = x_0 - \\frac{f'(x_0)}{f''(x_0)},\\tag{1}$$\n",
    "\n",
    "Repeat the process iteratively. Number of iterations $n$ is usually also a parameter. \n",
    "\n",
    "Let's optimize function $f\\left(x\\right)=e^x - \\log(x)$ (defined for $x>0$) using Newton's method. To implement it in the code, define function $f\\left(x\\right)=e^x - \\log(x)$, its first and second derivatives $f'(x)=e^x - \\frac{1}{x}$, $f''(x)=e^x + \\frac{1}{x^2}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "314b980f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(1.6) = 4.483028795149379\n",
      "f'(1.6) = 4.328032424395115\n",
      "f''(1.6) = 5.343657424395115\n"
     ]
    }
   ],
   "source": [
    "def f_example_1(x):\n",
    "    return np.exp(x) - np.log(x)\n",
    "\n",
    "def dfdx_example_1(x):\n",
    "    return np.exp(x) - 1/x\n",
    "\n",
    "def d2fdx2_example_1(x):\n",
    "    return np.exp(x) + 1/(x**2)\n",
    "\n",
    "x_0 = 1.6\n",
    "print(f\"f({x_0}) = {f_example_1(x_0)}\")\n",
    "print(f\"f'({x_0}) = {dfdx_example_1(x_0)}\")\n",
    "print(f\"f''({x_0}) = {d2fdx2_example_1(x_0)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d69f6ee0",
   "metadata": {},
   "source": [
    "Plot the function to visualize the global minimum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "905afb0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 576x288 with 1 Axes>,\n",
       " <AxesSubplot: xlabel='$x$', ylabel='$f\\\\,(x)$'>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_f(x_range, y_range, f, ox_position):\n",
    "    x = np.linspace(*x_range, 100)\n",
    "    fig, ax = plt.subplots(1,1,figsize=(8,4))\n",
    "\n",
    "    ax.set_ylim(*y_range)\n",
    "    ax.set_xlim(*x_range)\n",
    "    ax.set_ylabel('$f\\,(x)$')\n",
    "    ax.set_xlabel('$x$')\n",
    "    ax.spines['left'].set_position('zero')\n",
    "    ax.spines['bottom'].set_position(('data', ox_position))\n",
    "    ax.spines['right'].set_color('none')\n",
    "    ax.spines['top'].set_color('none')\n",
    "    ax.xaxis.set_ticks_position('bottom')\n",
    "    ax.yaxis.set_ticks_position('left')\n",
    "    ax.autoscale(enable=False)\n",
    "    \n",
    "    pf = ax.plot(x, f(x), 'k')\n",
    "    \n",
    "    return fig, ax\n",
    "\n",
    "plot_f([0.001, 2.5], [-0.3, 13], f_example_1, 0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f3686a8",
   "metadata": {},
   "source": [
    "Implement Newton's method described above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "103eb240",
   "metadata": {},
   "outputs": [],
   "source": [
    "def newtons_method(dfdx, d2fdx2, x, num_iterations=100):\n",
    "    for iteration in range(num_iterations):\n",
    "        x = x - dfdx(x) / d2fdx2(x)\n",
    "        print(x)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e94e6071",
   "metadata": {},
   "source": [
    "In addition to the first and second derivatives, there are two other parameters in this implementation: number of iterations `num_iterations`, initial point `x`. To optimize the function, set up the parameters and call the defined function gradient_descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5f41dab9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7900617721793732\n",
      "0.5436324685389214\n",
      "0.5665913613835818\n",
      "0.567143002403454\n",
      "0.5671432904097056\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "0.5671432904097838\n",
      "Newton's method result: x_min = 0.5671432904097838\n"
     ]
    }
   ],
   "source": [
    "num_iterations_example_1 = 25; x_initial = 1.6\n",
    "newtons_example_1 = newtons_method(dfdx_example_1, d2fdx2_example_1, x_initial, num_iterations_example_1)\n",
    "print(\"Newton's method result: x_min =\", newtons_example_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47e0c03e",
   "metadata": {},
   "source": [
    "You can see that starting from the initial point $x_0 = 1.6$ Newton's method converges after $6$ iterations. You could actually exit the loop when there is no significant change of $x$ each step (or when first derivative is close to zero).\n",
    "\n",
    "What if gradient descent was used starting from the same intial point?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e77a4ff0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1671967575604887\n",
      "0.9315747895403638\n",
      "0.7850695373565493\n",
      "0.693190848956033\n",
      "0.6374425307430822\n",
      "0.6051557294974615\n",
      "0.5872487093998153\n",
      "0.5776311173426577\n",
      "0.5725707323584608\n",
      "0.5699397792550739\n",
      "0.5685808560397663\n",
      "0.5678813962508925\n",
      "0.5675220281938029\n",
      "0.567337566350933\n",
      "0.5672429290172856\n",
      "0.567194387884144\n",
      "0.5671694934881042\n",
      "0.5671567271988156\n",
      "0.5671501806396171\n",
      "0.5671468236191124\n",
      "0.5671451021825211\n",
      "0.5671442194561769\n",
      "0.5671437668086716\n",
      "0.5671435346987772\n",
      "0.5671434156768685\n",
      "Gradient descent result: x_min = 0.5671434156768685\n"
     ]
    }
   ],
   "source": [
    "def gradient_descent(dfdx, x, learning_rate=0.1, num_iterations=100):\n",
    "    for iteration in range(num_iterations):\n",
    "        x = x - learning_rate * dfdx(x)\n",
    "        print(x)\n",
    "    return x\n",
    "\n",
    "num_iterations = 25; learning_rate = 0.1; x_initial = 1.6\n",
    "# num_iterations = 25; learning_rate = 0.2; x_initial = 1.6\n",
    "gd_example_1 = gradient_descent(dfdx_example_1, x_initial, learning_rate, num_iterations)\n",
    "print(\"Gradient descent result: x_min =\", gd_example_1) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37d76af5",
   "metadata": {},
   "source": [
    "Gradient descent method has an extra parameter `learning_rate`. If you take it equal to `0.1` in this example, the method will start to converge after about $15$ iterations (aiming for an accuracy of 4-5 decimal places). If you increase it to $0.2$, gradient descent will converge within about $12$ iterations, which is still slower than Newton's method. \n",
    "\n",
    "So, those are disadvantages of gradient descent method in comparison with Newton's method: there is an extra parameter to control and it converges slower. However it has an advantage - in each step you do not need to calculate second derivative, which in more complicated cases is quite computationally expensive to find. So, one step of gradient descent method is easier to make than one step of Newton's method.\n",
    "\n",
    "This is the reality of numerical optimization - convergency and actual result depend on the initial parameters. Also, there is no \"perfect\" algorithm - every method will have advantages and disadvantages."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a08f02b9",
   "metadata": {},
   "source": [
    "<a name='2'></a>\n",
    "## 2 - Function in Two Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13ae722c",
   "metadata": {},
   "source": [
    "In case of a function in two variables, Newton's method will require even more computations. Starting from the intial point $(x_0, y_0)$, the step to the next point shoud be done using the expression: \n",
    "\n",
    "$$\\begin{bmatrix}x_1 \\\\ y_1\\end{bmatrix} = \\begin{bmatrix}x_0 \\\\ y_0\\end{bmatrix} - \n",
    "H^{-1}\\left(x_0, y_0\\right)\\nabla f\\left(x_0, y_0\\right),\\tag{2}$$\n",
    "\n",
    "where $H^{-1}\\left(x_0, y_0\\right)$ is an inverse of a Hessian matrix at point $(x_0, y_0)$ and $\\nabla f\\left(x_0, y_0\\right)$ is the gradient at that point.\n",
    "\n",
    "Let's implement that in the code. Define the function $f(x, y)$ like in the videos, its gradient and Hessian:\n",
    "\n",
    "\\begin{align}\n",
    "f\\left(x, y\\right) &= x^4 + 0.8 y^4 + 4x^2 + 2y^2 - xy - 0.2x^2y,\\\\\n",
    "\\nabla f\\left(x, y\\right) &= \\begin{bmatrix}4x^3 + 8x - y - 0.4xy \\\\ 3.2y^3 + 4y - x - 0.2x^2\\end{bmatrix}, \\\\\n",
    "H\\left(x, y\\right) &= \\begin{bmatrix}12x^2 + 8 - 0.4y && -1 - 0.4x \\\\ -1 - 0.4x && 9.6y^2 + 4\\end{bmatrix}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a5dd8cc2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(4, 4) = 528.0\n",
      "grad f(4, 4) = \n",
      "[[277.6]\n",
      " [213.6]]\n",
      "H(4, 4) = \n",
      "[[198.4  -2.6]\n",
      " [ -2.6 157.6]]\n"
     ]
    }
   ],
   "source": [
    "def f_example_2(x, y):\n",
    "    return x**4 + 0.8*y**4 + 4*x**2 + 2*y**2 - x*y -0.2*x**2*y\n",
    "\n",
    "def grad_f_example_2(x, y):\n",
    "    return np.array([[4*x**3 + 8*x - y - 0.4*x*y],\n",
    "                     [3.2*y**3 +4*y - x - 0.2*x**2]])\n",
    "\n",
    "def hessian_f_example_2(x, y):\n",
    "    hessian_f = np.array([[12*x**2 + 8 - 0.4*y, -1 - 0.4*x],\n",
    "                         [-1 - 0.4*x, 9.6*y**2 + 4]])\n",
    "    return hessian_f\n",
    "\n",
    "x_0, y_0 = 4, 4\n",
    "print(f\"f{x_0, y_0} = {f_example_2(x_0, y_0)}\")\n",
    "print(f\"grad f{x_0, y_0} = \\n{grad_f_example_2(x_0, y_0)}\")\n",
    "print(f\"H{x_0, y_0} = \\n{hessian_f_example_2(x_0, y_0)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53b87b92",
   "metadata": {},
   "source": [
    "Run the following cell to plot the function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1d243fba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 720x360 with 2 Axes>,\n",
       " <AxesSubplot: xlabel='$x$', ylabel='$y$'>,\n",
       " <Axes3DSubplot: xlabel='$x$', ylabel='$y$', zlabel='$f$'>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_f_cont_and_surf(f):\n",
    "    \n",
    "    fig = plt.figure( figsize=(10,5))\n",
    "    fig.canvas.toolbar_visible = False\n",
    "    fig.canvas.header_visible = False\n",
    "    fig.canvas.footer_visible = False\n",
    "    fig.set_facecolor('#ffffff')\n",
    "    gs = GridSpec(1, 2, figure=fig)\n",
    "    axc = fig.add_subplot(gs[0, 0])\n",
    "    axs = fig.add_subplot(gs[0, 1],  projection='3d')\n",
    "    \n",
    "    x_range = [-4, 5]\n",
    "    y_range = [-4, 5]\n",
    "    z_range = [0, 1200]\n",
    "    x = np.linspace(*x_range, 100)\n",
    "    y = np.linspace(*y_range, 100)\n",
    "    X,Y = np.meshgrid(x,y)\n",
    "    \n",
    "    cont = axc.contour(X, Y, f(X, Y), cmap='terrain', levels=18, linewidths=2, alpha=0.7)\n",
    "    axc.set_xlabel('$x$')\n",
    "    axc.set_ylabel('$y$')\n",
    "    axc.set_xlim(*x_range)\n",
    "    axc.set_ylim(*y_range)\n",
    "    axc.set_aspect(\"equal\")\n",
    "    axc.autoscale(enable=False)\n",
    "    \n",
    "    surf = axs.plot_surface(X,Y, f(X,Y), cmap='terrain', \n",
    "                    antialiased=True,cstride=1,rstride=1, alpha=0.69)\n",
    "    axs.set_xlabel('$x$')\n",
    "    axs.set_ylabel('$y$')\n",
    "    axs.set_zlabel('$f$')\n",
    "    axs.set_xlim(*x_range)\n",
    "    axs.set_ylim(*y_range)\n",
    "    axs.set_zlim(*z_range)\n",
    "    axs.view_init(elev=20, azim=-100)\n",
    "    axs.autoscale(enable=False)\n",
    "    \n",
    "    return fig, axc, axs\n",
    "\n",
    "plot_f_cont_and_surf(f_example_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88731f3c",
   "metadata": {},
   "source": [
    "Newton's method $(2)$ is implemented in the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f2f020fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def newtons_method_2(f, grad_f, hessian_f, x_y, num_iterations=100):\n",
    "    for iteration in range(num_iterations):\n",
    "        x_y = x_y - np.matmul(np.linalg.inv(hessian_f(x_y[0,0], x_y[1,0])), grad_f(x_y[0,0], x_y[1,0]))\n",
    "        print(x_y.T)\n",
    "    return x_y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "775700eb",
   "metadata": {},
   "source": [
    "Now run the following code to find the minimum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4d3066a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.58273866 2.62128884]]\n",
      "[[1.59225691 1.67481611]]\n",
      "[[0.87058917 1.00182107]]\n",
      "[[0.33519431 0.49397623]]\n",
      "[[0.04123585 0.12545903]]\n",
      "[[0.00019466 0.00301029]]\n",
      "[[-2.48536390e-08  3.55365461e-08]]\n",
      "[[ 4.15999751e-17 -2.04850948e-17]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "[[0. 0.]]\n",
      "Newton's method result: x_min, y_min = [[0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "num_iterations_example_2 = 25; x_y_initial = np.array([[4], [4]])\n",
    "newtons_example_2 = newtons_method_2(f_example_2, grad_f_example_2, hessian_f_example_2, \n",
    "                                     x_y_initial, num_iterations=num_iterations_example_2)\n",
    "print(\"Newton's method result: x_min, y_min =\", newtons_example_2.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66c1cb88",
   "metadata": {},
   "source": [
    "In this example starting from the initial point $(4, 4)$ it will converge after about $9$ iterations. Try to compare it with the gradient descent now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "61f82d17",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.552 -0.272]]\n",
      "[[-1.00667816 -0.27035727]]\n",
      "[[-0.76722601 -0.26354393]]\n",
      "[[-0.61199381 -0.2542789 ]]\n",
      "[[-0.49957833 -0.24362609]]\n",
      "[[-0.41356991 -0.23220381]]\n",
      "[[-0.34561558 -0.22041345]]\n",
      "[[-0.29081322 -0.20852957]]\n",
      "[[-0.24600097 -0.19674484]]\n",
      "[[-0.20899755 -0.1851958 ]]\n",
      "[[-0.17822189 -0.17397885]]\n",
      "[[-0.15248504 -0.1631609 ]]\n",
      "[[-0.13086798 -0.15278673]]\n",
      "[[-0.11264557 -0.14288438]]\n",
      "[[-0.09723686 -0.13346909]]\n",
      "[[-0.08417097 -0.12454632]]\n",
      "[[-0.07306297 -0.11611405]]\n",
      "[[-0.0635961  -0.10816464]]\n",
      "[[-0.05550841 -0.10068622]]\n",
      "[[-0.04858239 -0.09366384]]\n",
      "[[-0.04263691 -0.08708035]]\n",
      "[[-0.03752071 -0.08091713]]\n",
      "[[-0.03310722 -0.07515463]]\n",
      "[[-0.02929035 -0.06977285]]\n",
      "[[-0.02598099 -0.06475166]]\n",
      "[[-0.02310421 -0.06007107]]\n",
      "[[-0.02059686 -0.05571146]]\n",
      "[[-0.01840572 -0.05165372]]\n",
      "[[-0.01648577 -0.04787936]]\n",
      "[[-0.01479896 -0.04437062]]\n",
      "[[-0.01331303 -0.04111048]]\n",
      "[[-0.01200059 -0.03808275]]\n",
      "[[-0.01083835 -0.03527203]]\n",
      "[[-0.0098065  -0.03266375]]\n",
      "[[-0.00888809 -0.03024417]]\n",
      "[[-0.00806868 -0.02800031]]\n",
      "[[-0.00733584 -0.02591999]]\n",
      "[[-0.00667896 -0.02399178]]\n",
      "[[-0.00608885 -0.02220496]]\n",
      "[[-0.00555764 -0.02054949]]\n",
      "[[-0.00507848 -0.019016  ]]\n",
      "[[-0.00464546 -0.01759575]]\n",
      "[[-0.00425344 -0.01628056]]\n",
      "[[-0.00389794 -0.01506284]]\n",
      "[[-0.00357505 -0.01393549]]\n",
      "[[-0.00328135 -0.01289193]]\n",
      "[[-0.00301383 -0.01192602]]\n",
      "[[-0.00276985 -0.01103207]]\n",
      "[[-0.00254707 -0.01020478]]\n",
      "[[-0.00234342 -0.00943925]]\n",
      "[[-0.00215708 -0.0087309 ]]\n",
      "[[-0.00198642 -0.00807551]]\n",
      "[[-0.00182997 -0.00746915]]\n",
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      "[[-2.68929479e-11 -1.13920355e-10]]\n",
      "[[-2.48684833e-11 -1.05344586e-10]]\n",
      "[[-2.29964177e-11 -9.74143886e-11]]\n",
      "[[-2.12652786e-11 -9.00811659e-11]]\n",
      "[[-1.96644574e-11 -8.32999782e-11]]\n",
      "[[-1.81841438e-11 -7.70292691e-11]]\n",
      "[[-1.68152661e-11 -7.12306104e-11]]\n",
      "[[-1.55494358e-11 -6.58684669e-11]]\n",
      "[[-1.43788954e-11 -6.09099783e-11]]\n",
      "[[-1.32964717e-11 -5.63247579e-11]]\n",
      "[[-1.22955314e-11 -5.20847067e-11]]\n",
      "[[-1.13699405e-11 -4.81638408e-11]]\n",
      "[[-1.05140268e-11 -4.45381324e-11]]\n",
      "[[-9.72254518e-12 -4.11853623e-11]]\n",
      "[[-8.99064520e-12 -3.80849842e-11]]\n",
      "[[-8.31384165e-12 -3.52179984e-11]]\n",
      "[[-7.68798695e-12 -3.25668353e-11]]\n",
      "[[-7.10924575e-12 -3.01152483e-11]]\n",
      "Gradient descent result: x_min, y_min = [[-7.10924575e-12]\n",
      " [-3.01152483e-11]]\n"
     ]
    }
   ],
   "source": [
    "def gradient_descent_2(grad_f, x_y, learning_rate=0.1, num_iterations=100):\n",
    "    for iteration in range(num_iterations):\n",
    "        x_y = x_y - learning_rate * grad_f(x_y[0,0], x_y[1,0])\n",
    "        print(x_y.T)\n",
    "    return x_y\n",
    "\n",
    "num_iterations_2 = 300; learning_rate_2 = 0.02; x_y_initial = np.array([[4], [4]])\n",
    "# num_iterations_2 = 300; learning_rate_2 = 0.03; x_y_initial = np.array([[4], [4]])\n",
    "gd_example_2 = gradient_descent_2(grad_f_example_2, x_y_initial, learning_rate_2, num_iterations_2)\n",
    "print(\"Gradient descent result: x_min, y_min =\", gd_example_2) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fa2602d",
   "metadata": {},
   "source": [
    "Obviously, gradient descent will converge much slower than Newton's method. And trying to increase learning rate, it might not even work at all. This illustrates again the disadvantages of gradient descent in comparison with Newton's method. However, note, that Newton's method required calculation of an inverted Hessian matrix, which is a very computationally expensive calculation to perform when you have, say, a thousand of parameters.\n",
    "\n",
    "Well done on finishing this lab!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c418025",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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